1. Technical Field
The present invention relates to a lens optical system and a photoelectric encoder. More particularly, the present invention relates to a lens optical system capable of relaxing a variation of a focal length of a plastic lens due to a temperature change and one-side and both-side telecentric optical systems containing the lens optical system which are suitable for a linear scale and various optical equipments. Furthermore, the present invention relates to a photoelectric encoder containing them.
2. Description of Related Art
As one of optical lenses used in the optical instrument, there is the lens that is made of plastics (hereinafter referred to as “plastic lens”). This plastic lens has advantages that this lens is relatively inexpensive and also an aspheric surface can be easily shaped. However, on the other hand, the plastic lens has a disadvantage that a variation of a focal position due to a temperature change is large.
As the main factor in the variation of the focal position, a change of a refractive index of the lens due to a temperature change and a change in lens curvature due to a thermal expansion can be listed. In other work explanation will be made by taking a plastic lens 10 as the biconvex spherical lens shown in FIG. 1 as an example. A relationship be a focal lend f and a refractive index n, lens curvatures R1, R2 on the incident side and the emergent side, and a lens thickness d is given by following Equation (1).1/f=(n−1)×{(1/R1)−(1/R2)+{(n−1)2/n}×{d/(R1×R2)}  (1)
Normally the refractive index n decreases and also the lens cures R1, R2 increase when the temperature rises. Therefore, both changes act in the direction to lengthen a focal length f. In contrast, both changes act in the direction to shorten a focal length f when the temperature falls.
Also, normally a change of the refractive index of the plastic lens and a variation of the focal length f due to the thermal expansion are ten times or more those of a lens that is made of glass (hereinafter referred to as “glass lens”), and these changes have great influences on lens performance. For this reason, some measure to relax such influences need to be taken.
For example, in Reference 1, it is set forth that a variation of the focal position due to a change of the refractive index can be cancelled by employing the hybrid lens in which plural pieces of lenses such as a convex lens, a concave lens, etc., whose lens profiles are different mutually, are aligned in combination.
[Reference 1] JP-A-943508
However, the hybrid lens set forth in Reference 1 has such a problem that an increase in cost and a difficulty of optical axis adjustment are caused due to an increase in the number of lenses.